Question

A block of wood floats in water with ${\left(\frac{4}{5}\right)}^{th}$ of its volume submerged. If the same block just floats in a liquid, the density of the liquid (in kg m${}^{-3}$) is:

• A. 1250
• B. 600
• C. 400
• D. 800

Answer 1

The correct option is D 800

According to Archimede's principle Weight of the body = Weight of the liquid displaced Let $V$ be volume of block.
In water, $V{\rho }_{block}g=\left(\frac{4}{5}V\right){\rho }_{water}g$
${\rho }_{block}=\frac{4}{5}{\rho }_{weter}$ ....(i)
In liquid, $V{\rho }_{block}g=V{\rho }_{liquid}g$
${\rho }_{block}={\rho }_{liquid}$ .....(ii)
From (i) and (ii), we get
${\rho }_{Liquid}=\frac{4}{5}{\rho }_{water}=\frac{4}{5}\times {10}^{3}kg{m}^{-3}=800kg{m}^{-3}$